Comment on soft-pion emission in DVCS

The soft-pion theorem for pion production in deeply virtual Compton scattering, derived by Guichon, Mosse and Vanderhaegen, is shown to be consistent with chiral perturbation theory. Chiral symmetry requires that the nonsinglet operators corresponding to spin-independent and spin-dependent parton distributions have the same anomalous dimensions in cases where those operators are related by chiral transformations. In chiral perturbation theory, their scale-dependences can thus be absorbed in the coefficents of the corresponding effective operators, without affecting their chiral structures.Comment: 2 pages, RevTe

Radiative Kaon Decays K±→π±π0γK^\pm\to\pi^\pm\pi^0\gamma and Direct CP Violation

It is stressed that a measurement of the electric dipole amplitude for direct photon emission in \kpm decays through its interference with inner bremsstrahlung is important for differentiating among various models. Effects of amplitude CP violation in the radiative decays of the charged kaon are analyzed in the Standard Model in conjunction with the large $N_c$ approach. We point out that gluon and electromagnetic penguin contributions to the CP-violating asymmetry between the Dalitz plots of \kpm are of equal weight. The magnitude of CP asymmetry ranges from $2\times 10^{-6}$ to $1\times 10^{-5}$ when the photon energy in the kaon rest frame varies from 50 MeV to 170 MeV.Comment: Latex, 11 pages, ITP-SB-93-36, IP-ASTP-22-9

Aspects of chiral pion-nucleon physics

The next-to-leading order chiral pion-nucleon Lagrangian contains seven finite low-energy constants. Two can be fixed from the nucleon anomalous magnetic moments and another one from the quark mass contribution to the neutron-proton mass splitting. We find a set of nine observables, which to one loop order do only depend on the remaining four dimension two couplings. These are then determined from a best fit. We also show that their values can be understood in terms of resonance exchange related to $\Delta$ excitation as well as vector and scalar meson exchange. In particular, we discuss the role of the fictitious scalar-isoscalar meson. We also investigate the chiral expansion of the two P-wave scattering volumes $P_1^-$ and $P_2^+$ as well as the isovector S-wave effective range parameter $b^-$. The one-loop calculation is in good agreement with the data. The difference $P_1^- - P_2^+$ signals chiral loop effects in the $\pi N$ P-waves. The calculated D- and F-wave threshold parameters compare well with the empirical values.Comment: 19 pp, LaTeX, enlarged and revised version, title changed, minor corrections in section 4, more detailed discussion in section 5, additional results in sec. 6 and the appendix, accepted for publication in Nucl. Phys.

Final-sate radiation in electron-positron annihilation into a pion pair

The process of $e^+e^-$ annihilation into a $\pi^+\pi^-$ pair with radiation of a photon is considered. The amplitude of the reaction $e^+e^-\to\pi^+\pi^-\gamma$ consists of the model independent initial-state radiation (ISR) and model-dependent final-state radiation (FSR). The general structure of the FSR tensor is constructed from Lorentz covariance, gauge invariance and discrete symmetries in terms of the three invariant functions. To calculate these functions we apply Chiral Perturbation Theory (ChPT) with vector and axial-vector mesons. The contribution of $e^+e^-\to\pi^+\pi^-\gamma$ process to the muon anomalous magnetic moment is evaluated, and results are compared with the dominant contribution in the framework of a hybrid model, consisting of VMD and point-like scalar eletrodynamics. The developed approach allows us also to calculate the $\pi^+\pi^-$ charge asymmetry.Comment: 21 pages, 8 figure

General CP Violation in Minimal Left-Right Symmetric Model and Constraints on the Right-Handed Scale

In minimal left-right symmetric theories, the requirement of parity invariance allows only one complex phase in the Higgs potential and one in the Yukawa couplings, leading to a two-phase theory with both spontaneous and explicit CP violations. We present a systematic way to solve the right-handed quark mixing matrix analytically in this model and find that the leading order solution has the same hierarchical structure as the left-handed CKM matrix with one more CP-violating phase coming from the complex Higgs vev. Armed with this explicit right-handed mixing matrix, we explore its implications for flavor changing and conserving processes in detail, low-energy CP-violating observables in particular. We report an improved lower bound on the $W_R$ mass of 2.5 TeV from $\Delta M_K$ and $\Delta M_{B}$, and a somewhat higher bound (4 TeV) from kaon decay parameters $\epsilon$, $\epsilon'$, and neutron electric dipole moment. The new bound on the flavor-changing neutral Higgs mass is 25 TeV.Comment: 35 pages, 14 figure

The vector form factor of the pion from unitarity and analyticity: a model-independent approach

We study a model-independent parameterization of the vector pion form factor that arises from the constraints of analyticity and unitarity. Our description should be suitable up to sqrt(s) ~ 1.2 GeV and allows a model-independent determination of the mass of the rho(770) resonance, M(rho) = (775.1 +- 0.5) MeV. We analyse the experimental data on tau(-) -> pion(-) pion(0) neutrino(tau), in this framework, and its consequences on the low-energy observables worked out by chiral perturbation theory. An evaluation of the two-pion contribution to the anomalous magnetic moment of the muon, a_muon, and to the fine structure constant, alpha(M(Z)^2), is also performed.Comment: 1+15 pages, 2 figure

Ubiquitous CP violation in a top-inspired left-right model

We explore CP violation in a Left-Right Model that reproduces the quark mass and CKM rotation angle hierarchies in a relatively natural way by fixing the bidoublet Higgs VEVs to be in the ratio m_b:m_t. Our model is quite general and allows for CP to be broken by both the Higgs VEVs and the Yukawa couplings. Despite this generality, CP violation may be parameterized in terms of two basic phases. A very interesting feature of the model is that the mixing angles in the right-handed sector are found to be equal to their left-handed counterparts to a very good approximation. Furthermore, the right-handed analogue of the usual CKM phase delta_L is found to satisfy the relation delta_R \approx delta_L. The parameter space of the model is explored by using an adaptive Monte Carlo algorithm and the allowed regions in parameter space are determined by enforcing experimental constraints from the K and B systems. This method of solution allows us to evaluate the left- and right-handed CKM matrices numerically for various combinations of the two fundamental CP-odd phases in the model. We find that all experimental constraints may be satisfied with right-handed W and Flavour Changing Neutral Higgs masses as low as about 2 TeV and 7 TeV, respectively.Comment: 37 pages, 13 figure

On the analysis of the pion--nucleon σ\sigma--term: The size of the remainder at the Cheng--Dashen point

We calculate the one--loop contributions of order $M_\pi^4$ to the difference $\Delta_R$ between the on--shell pion--nucleon scattering amplitude $\bar{D}^+(0,2M_\pi^2)$ at the Cheng--Dashen point $\nu =0$, $t=2M_\pi^2$ and the scalar form factor $\sigma (2M_\pi^2)$ in the framework of heavy baryon chiral perturbation theory. We proof that to this order $\Delta_R$ contains $no$ chiral logarithms and therefore it vanishes simply as $M_\pi^4$ in the chiral limit. Numerically, we find as an upper limit $\Delta_R \simeq 2\,$MeV.Comment: 7 pp, LaTeX, uses epsf, 1 figure in separate PS fil

Peripheral Nucleon-Nucleon Phase Shifts and Chiral Symmetry

Within the one-loop approximation of baryon chiral perturbation theory we calculate all one-pion and two-pion exchange contributions to the nucleon-nucleon interaction. In fact we construct the elastic NN-scattering amplitude up to and including third order in small momenta. The phase shifts with orbital angular momentum $L\geq2$ and the mixing angles with $J\geq2$ are given parameterfree and thus allow for a detailed test of chiral symmetry in the two-nucleon system. We find that for the D-waves the $2\pi$-exchange corrections are too large as compared with empirical phase shifts, signaling the increasing importance of shorter range effects in lower partial waves. For higher partial waves, especially for G-waves, the model independent $2\pi$-exchange corrections bring the chiral prediction close to empirical NN phase shifts. We propose to use the chiral NN phase shifts with $L\geq 3$ as input in a future phase shift analysis. Furthermore, we compute the irreducible two-pion exchange NN-potentials in coordinate space. They turn out to be of van-der-Waals type, with exponential screening of two-pion mass range.Comment: 30 pages, TeX,12 figures in ps , submitted to Nucl. Phys.

One-loop vertex integrals in heavy-particle effective theories

We give a complete analytical computation of three-point one-loop integrals with one heavy propagator, up to the third tensor rank, for arbitrary values of external momenta and masses.Comment: 10 pages, Latex, to appear in J. Phys.